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Absorption of sulfur dioxide in dilute aqueous solutions of sulfuric and hydrochloric acid
r,a ELSEVIER
Fluid Phase Equilibria 141 (1997) 221-233
Absorption of sulfur dioxide in dilute aqueous solutions of sulfuric and hydrochloric acid J. Krissmann *, M.A. Siddiqi, K. Lucas Department q)cThermodynamics, FB 7, Gerhard Mercator University Duisburg, Duisburg 47048, Germany
Received 3 March 1997; accepted 14 August 1997
Abstract Spectrophotometric measurements of combined phase and chemical equilibrium have been performed for S O 2 + HzSO 4 -F H 2 0 and SO 2 + HCI + H 2 0 systems at 298 K and atmospheric pressure. The vapour and liquid phases have been analysed in situ using a fibre optic based technique described in an earlier publication. The measurements have been performed up to an equilibrium partial pressure of about 1 kPa for sulfur dioxide. The concentration range of the acids have been varied up to 0.5 M for H 2 S O 4 and 1.0 M for HCI. A thermodynamic model is presented which allows the interpolation and the extrapolation of the experimental results. The calculated partial pressures of SO 2 in the SO 2 + H2SO 4 + H 2 0 system are compared with existing literature values. The experimental results for the SO 2 + HCI + H 2 0 system show an anomaly in the uv-spectrum of molecular dissolved sulfur dioxide. The absorption band for SO 2 is shifted towards higher wavelength. This effect is interpreted in terms of the formation of a weak complex SO2C1-. © 1997 Elsevier Science B.V. Kevwords: Vapour-liquid equilibria; Chemical equilibria; Spectroscopy; Data; Method of calculation
1. Introduction Flue gases from coal fired power plants or incinerating plants contain pollutants like SO 2 and HCl. A typical way to remove these pollutants is the wet flue gas desulfurisation, which is a complex physical and chemical absorption process. In technical applications, part of the liquid is often recirculated within the absorber. As a consequence of this, there is an increase of the amount of chloride and sulfate ions in relation to the dissolved sulfur dioxide. There is a lack of reliable data for such important binary and ternary systems in literature.
* Corresponding author. 0378-3812/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S 0 3 7 8 - 3 8 1 2 ( 9 7 ) 0 0 2 0 3 - 3
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J. Krissmann et al. /
Fluid Phase Equilibria 141 (1997) 221-233
Therefore, spectrophotometric measurements of the phase and chemical equilibrium for certain selected systems containing SO 2 have been performed. For this, a newly developed apparatus, which allows the simultaneous in situ analysis of gas and liquid phase, has been used to determine the equilibrium partial pressure of SO 2 and the amount of molecular dissolved sulfur dioxide in SO 2 + H2SO 4 + H 2 0 and SO 2 + HC1 + H20 systems. It is shown that the additional specification of the liquid phase yields a deeper insight into the reactions occurring in solution. A thermodynamic model based on Pitzer's theory is presented to correlate and extrapolate the experimental results.
2. Experimental procedure The measurements were carried out using the apparatus described in a previous communication [ 1]. This apparatus was placed inside an air thermostat to accomplish the measurements at a constant temperature of 298 K. Standard gas mixtures from Messer-Griesheim with an uncertainty of _+0.5% were used to prepare the gaseous mixtures of desired compositions. The acidic solutions were prepared from certified molar mixtures of acids from Fluka (accuracy better than ± 0.1%) by diluting these with deionised water. The solution was degassed with nitrogen, which was saturated with H20 by bubbling through deionised water, to remove any dissolved carbon dioxide and oxygen. The concentration of the aqueous solution was checked additionally using ion chromatography for chloride and sulfate ions. As the calculations are done on a molal basis, the molarities of the solutions were converted to molalities using tabulated density data [2]. The method for the measurements was basically the same as described earlier except that this time the simultaneous analysis of the liquid phase was performed by circulating it via insulated tubing through a standard cuvette placed inside another uv-spectrophotometer (Shimadzu UVPC 2102). With increasing acid concentrations, it was necessary to use an optical length of 1 mm to cope with the high absorbance by the solutions. The reaction was started by opening the appropriate valves and circulating the gas mixture through the aqueous solution. After attainment of the thermodynamic equilibrium (indicated by a non-changing spectrum over a period of time), the spectrum of the gaseous phase was taken by scanning through the wavelength range of 220 nm to 400 nm with the help of the uv-diode array spectrophotometer and evaluated as described before [1] to determine the concentration of sulfur dioxide in the vapour phase, C 2 (SO2), in equilibrium with the liquid. The equilibrium partial pressure (reference pressure: p0 = 100 kPa), was then calculated by p0
p(SO2)/kPa = --. P2
6 2 ( 8 0 2 ) . R- T2
(1)
where P2, T2 and C 2 (802) denote the pressure (kPa), temperature (K) and SO 2 concentration in the gas phase (mol dm -3) at equilibrium. Finally, the spectrum of the liquid phase (220-400 nm) was taken by circulating it through the cuvette of the second uv-spectrophotometer. Evaluation of this spectrum furnished the specification of the liquid phase. The calibration for the liquid phase depends on the components present and will be described in context with the results.
J. Krissmann et al. / Fluid Phase Equilibria 141 ~1997) 221-233
.-3
3. Thermodynamic model The absorption of sulfur dioxide in aqueous solutions of H2SO 4 and HCI in the absence of oxygen can be described using the following equations SO2(g) ~ SO2(aq )
(A)
SO2(aq) + H20(1 ) ~ H+(aq) + HSO3(aq)
(B)
HeSO4(aq ) ~ H+ (aq) + HSOa(aq)
(c)
HSO 4 (aq) ~ H + (aq) + SO 2- (aq)
(D)
nCl(aq) ~ H+(aq) + Cl-(aq)
(E)
SO2(aq) ~ Cl-(aq) ~ SO2Cl-(aq)
(F)
and
Eqs. (A) and (B) describe the physical absorption and the hydrolysis of sulfur dioxide [3]. The formation of sulfite (SO 2 ) and pyrosulfite ion ($20~-) is neglected because of the low pH of the solution and the low concentrations for SO 2 [1]. The first dissociation of sulfuric acid, Eq. (C), is assumed to be complete in the concentration range studied here [4,5], whereas for the second dissociation (Eq. (D)) the equilibrium constant is adopted from Pitzer's work [6]. The dissociation of the hydrogen chloride (Eq. (E)) is assumed to be complete as well, because of the high dilution [7]. Finally, Eq. (F) shows the formation of the weak complex SO2C1 . The justification for this reaction follows later in this section. Based on the assumed reaction scheme, the equilibrium constants for Eqs. (A), (B), (D) and (F) can be formulated as (-/so ~
,)/SO2(aq )
mso2(aq)
p0
4'so
Pso
""
KA(T) = fso. xB(r) =
a H , • aHSOg
,.,
=
aSO2(a q) " a H , O
KD(T ) .
aH+'aso~ . aso,c, aSO_,(aq) " a c I
"yH +" a/HSO g
m H ~" mHSO{
1
")/SOe(aq) " ")/H ~O
mso2(aq) " XH ,O
roll
TH+" Yso~ . .
mH+' mso ~
1
")/HSO£
mHSQ
mO
~-/HSO ~
KF(T ) =
(2)
=
Yso,o
mso,c,
'YSO2(aq) " ")/CI
m s o z ( a q ) " Ill('1
(3)
~'4) • m"
(5)
Here, (9 denotes the standard state of the pure substance, pO = 100 kPa and m ° = 1 tool kg ~. The mass balance for S ~v, S vl and C1 gives mso~_(tot ) = mso2(aq ) Jr- mHSO7 q-
msoec I
(6)
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J. Krissmann et al. / Fluid Phase Equilibria 141 (1997) 221-233
+ m(0) H2SO 4 = mHSO2 msog-
(7)
m(0) HC1 ~
(8)
mCl-
+
mso2cl
and the condition of electroneutrality for the solution leads to mn+-mcl -2.mso ~ -mnso;-mns
(9)
Q - - m s o ~ cr- = 0 .
The gas phase is treated like an ideal gas. The equilibrium concentrations of the species existing in the liquid phase may be obtained by solving these equations. However, the activity coefficients are not directly known. Starting from Pitzer's theory [8,9], considering the ion-ion, ion-molecule and molecule-molecule interactions and following the treatment of Edwards et al. [10], the following equation for the activity coefficient of any species i (ionic or molecular) is used lnyi=
-As(T)"
( f[ 1 ln(l+l,2fi))+2 z2 1 + 1,2~/I" + 1,----2
×(1-(1
+ 2v~)exp(-Zfi)))
z2 Y'.
412 jv~H20
" ~ ,nj(/3i~°)+ 13~jz) j~n2o 2--7-
Y'~ mjm~j~)(1-(1
+ 2v~ + 21)
k~H20
× exp( - 2v~)) Here,
z i denotes
(10)
the charge of the component i and I is the ionic strength of the solution, given as
1
I= -~" Y'~mi.zZi
(11)
i
The first term of Eq. (10) is derived from Debye-Htickel theory and describes the strong coulomb forces between the ions. The short range interactions between ion-ion, ion-molecule and moleculemolecule are represented by the other two terms. This model takes into account only the binary interaction parameters, which is justified for the low solute concentrations studied here [8]. The parameters for the ion-ion interaction are taken from literature for strong electrolytes [11,5], while the molecule-molecule and the molecule-ion interaction parameters are neglected. The parameter /3 (0) for the interaction between H + and SO2CI- does not exist in the literature and was, therefore, fitted to reproduce our results. Following Pitzer, the short range interaction parameters between ions of the same charge are set equal to zero. The Debye-Hiickel term is also a function of temperature and is taken from the work of Chen et al. [12]. Finally, the water activity is calculated as [10]
lna°n2o=Mn2o
( 2A~(T)'II5 1+i'_2~¢ff
-
y'~
]~
) mimj(~iT)+C3iT)exp(-Zv/-[))
i~e H20 j ~ H 2 0
-Mn2 o ~
mi
(12)
i~H20
The calculation is done iteratively, because the activity coefficients depend on the ionic strength which is itself a function of the molalities. The iteration is done until the activity coefficients of the solutes do not change significantly. The partial pressure can then be calculated from Eq. (2).
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J. Krissmann et al. / Fluid Phase Equilibria 141 (1997) 221-233
4. Results and discussion The experimental results for the partial pressure of SO 2 and the molality of undissociated sulfur dioxide mso2(aq ) in the SO 2 + H2SO 4 + H 2 0 system are shown in Table 1 and Figs. 1 and 2. The ion-ion interaction parameters used for the calculations are taken from literature and are listed in Table 2. The experimental and calculated values match very well. An influence of H 2 S Q on the uv-spectrum has been reported in more concentrated sulfuric acid [ 14]. At low H 2SO4 concentrations studied in this work, no such effect was noticed (cf. Fig. 2). Using this thermodynamic model, further calculations are done at other temperatures for a comparison with literature data. Parkinson [15] measured the solubility of SO 2 in water and aqueous solutions containing 0.058 M sulfuric acid at various temperatures. His results can be reproduced by our model within experimental error (Fig. 3). This places confidence in the extrapolation ability of the described model in terms of molality mso2ctot) and temperature. The temperature effect could be adequately described by considering the temperature dependence of Debye-H~ickel term and of the equilibrium constants of Eqs. (A), (B) and (D). The ion-ion interaction parameters are considered
Table I Phase and chemical equlibrium for SO 2 + H2SO 4 + H20 system CH~sQ (mol d i n - 3)
mso,oo, ) (tool kg - t )
T (K)
0.005 0.005 0.005 0.005 0.005 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.100 0. 100 0.100 0.100 0.100 0.51)0 0.500 0.500 0.500 0.500
0.00123 0.00455 0.00761 0.01066 0.01545 0.00092 0.00097 0.00335 0.00495 0.00593 0.00596 0.00824 0.01237 0.01253 0.00079 0.00401 0.00483 0.00787 0.01163 0.00081 0.00316 0.00485 0.00740 0.01112
298.35 298.55 298.05 298.35 298.25 298.25 298.05 298.45 298.15 298.35 298.15 298.25 298.05 298.15 298.15 298.15 298.05 298.15 298.15 298.15 298.25 298.05 298.05 298.25
Pso~ (kPa)
Pso2(calc) (kPa)
T * (K)
0.033 0.140 0.254 0.373 0.592 0.051 0.054 0.200 0.302 0.349 0.357 0.512 0.770 0.765 0.053 0.267 0.317 0.533 0.800 0.064 0.249 0.375 0.572 0.864
0.035 0.144 0.254 0.382 0.592 0.057 0.059 0.208 0.304 0.368 0.367 0.510 0.761 0.774 0.054 0.275 0.330 0.541 0.799 0.063 0.248 0.378 0.576 0.873
298.35 298.55 298.25 298.35 298.15 298.25 298.05 298.45 298.15 298.35 298.15 298.25 298.05 297.95 297.95 297.75 297.85 298.05 297.95 297.85 297.75 297.75 297.85 297.65
T* is the temperature of solution in the cuvette.
tHSO2(aq) I)
/nSO2(aq t(calc) I)
(tool kg
(mol kg -
-
0.00042 0.00175 0.00313 0.00466 0.00724 0.00069 0.00073 0.00253 0.00374 0.00448 0.00450 0.00624 /).00938 0.00950 0.00067 0.00338 0.00407 0.00664 0.00981 0.00078 0.00303 0.00466 0.00710 0.01067
0.00321 0.00738 0.00068 0.00369 0.00949 0.00960 0.00067 0.00336 0.00413 0.00660 0.00983 0.00080 0.00305 0.00464 0.00708 0.01067
J. Krissmann et al. / Fluid Phase Equilibria 141 (1997) 221-233
226
1, X 0.005rnolfl H2SO4 + 0.050mol/I H2SO4
0.8
/~ /
[] O.lOOmot/,.,so,
/
A 0.500mol;I HzSO4
/
/ ~
/ ,./
/ /
/
/
~_ 0.6
y_o.4
0.2
I
00
~
0.003
I
,
I
L
i
0.006 0.009 0.012 mso2(tot] / (mol/kg)
,
I
,
0.015
0.018
Fig. I. Combinedphase and chemicalequilibriumfor SO2 + H2SO4 4-H20 systemat 298 K.
independent of temperature. In Fig. 4, the available literature values at 298.15 K are compared with our results. The measurements of Hunger et al. [5] agree with the calculations done with our model, except for one point at 0.03 mol kg -~. The experimental values of Johnstone and Leppla [16] for SO 2 + H 2 0 and SO 2 + H2SO 4 + H 2 0 systems may be reproduced by our model with the exception of very dilute sulfuric acid solutions (0.0879 mol kg-J H2SO4).
0.018 0.015
/-
O SO2+H20[13] X 0.005mol/I H2504 + 0.050mol/I HzSO4
/~/" o
[] 0.100mol/I H,SO4 Z~0.500mol/I H2SO4
"~
/.~ ./~./"
100% SO2(aq) 7 / / ,/7/" j
F
/
. /
/
///,
0.0o9 ~0.006
.... /.
/.
0.003 0
0.003
0.006 0.009 0.012 mso2(lot) / (mol/kg)
0.015
0.018
Fig. 2. Molalityof moleculardissolved S O 2 in SO2 + H2SO4 4-H20 systemat 298 K.
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J. Krissmann et al. / Fluid Phase Equilibria 141 ( I997~ 221-233
Table 2 Parameters used in the model Equilibrium constants a n d D e b v e - Hiickel p a r a m e t e r at t,arious temperatures
298.15 K
294.25 K
305.35 K
1.228 0.0139 0.0105 O. 162 0.3909
1.421 0.0152 0.0119 -0.3883
0.955 0.{)116 0.0084
i
J
t-~(o, ~ij
H4 n~ H* H H+ All other interaction parameters
HSO:~ HSQ SO~ CISO2C1 are set equal to zero
KA KB KD Kr
A + / ( k g mol- ~)os
0.3962
Source [3] [3] [6] This wc,rk [12]
Interaction p a r a m e t e r s
Source
,G~]'
0.1500 0.2106 0.0217 0.1775 0.1741
0.4000 0.532/) 0.2945 0.5508
[5] [1 I1 [11] [1 I] This work
The experimental results for the SO 2 + HC1 + H 2° system are presented in Table 3 and Fig. 5. An examination of Fig. 5 shows that the partial pressure of SO 2 in the SO~ + HC1 + H+O system increases up to a concentration of 0.5 M HC1, but is lower at 1 M HC1. This decrease at 1 M HCI concentration can not be explained on the basis of the dissociation of SO2(aq). A careful study of the spectra of the liquid phase for the SO 2 + HC1 + H 2 0 system reveals that the uv-spectra show a
© 294.25K, SO2+H20 A 294.25K, 0.0580mol/IH2SO4 [] 305.35K, 0.0580mol/IHzSQ ~v3 Model ~
/" /
/
U ~
~
G_ "--2 cO
G_ 1
00
i 0.02
0.04
0.06
ms02(tot) / (mol/kcj) Fig. 3. Comparison of model calculations with literature data [ 15] at various temperatures.
228
J.
Krissmann et al. / Fluid Phase Equilibria 141 (1997) 221-233
2.5 O SO2+H20[16] [] 0.0879mol/kg H2SO4 [10] A 0.5174mol/kg H2SO4 [163 2 ~ 7 $.[030 mollkg H2SO4 [16] ...... Model • so,+mo
[5]
t ~ • 0.01 mol/I H2SO, [5] CL- J " o " -,z i , 0.20 m ol/I H2SO` [5] Model - ~
-
,//S~..'"
J
// ~
~
/
/ /
/
,./-."
0
,
-0
(fZ//..//
,,:~.// //" ;x-y,'" ,.,, ..
,,.¢~-//,"'" // // (///~////
-
05 -
,SS'~// / / / //////-/ /// ///,,/"~/"/
-
I
0.01
,
I
,
0.02 mso2(tot) / ( m o l / k g )
I
0.03
J
0.04
Fig. 4. Comparisonof model calculationswith literaturedata [5,16] at 298 K.
change in the peak structure depending upon the amount of hydrogen chloride in solution, when compared with the spectrum of molecular dissolved sulfur dioxide in pure water. It is observed that there is a shift of the peak maximum to greater wavelength (from 276 nm to nearly 280 nm) with increasing HC1 content in the solution. We attribute the above mentioned effects to be caused by the formation of a weak complex SOzC1-. The complexation of sulfur dioxide by halides ( S O z X - ) in acetonitrile, water and dimethyl sulfoxide solutions has been reported in the literature [17,18]. The formation of a complex like SO 2 • HC1 in aqueous solutions as well as in the vapour phase is also documented [19,20]. Both of these complexes are stochiometrically possible. In order to testify, whether the amount of total hydrogen chloride or chloride ion only is responsible for the described anomaly, we compare the liquid phase spectra for the SO 2 + HC1 + H 2 0 system and those for the SO 2 + CaC12 + H 2 0 system, reported elsewhere [21]. It is seen that both spectra are very much similar. To quantify this, a special mathematical algorithm called 'principal component analysis' (PCA) [22,23] is applied for comparison of the liquid phase spectra. The essential requirement for PCA is the existence of linear interactions between the variables. In uv-spectroscopy the Lambert-Beer law describes such a linear connection between the concentration of the light absorbing component i and the extinction
E(a)=
= i
c,.a
(13)
i
The assumption of a linear behaviour leads to the possibility of data reduction by transformation to a new appropriate coordinate system. The new axis (Fig. 6) lies in the direction of the maximum variation in the data set and is called principal component (PC~). In uv-spectroscopy, the whole
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J. Krissmann et al. / Fluid Phase Equilibria 141 (1997) 221-233
Table 3 Phase and chemical equilibrium for SO 2 + HC1 + H 20 system CHCl 3) (tool dm
T (K)
mso:(tot) (tool kg- i )
Pso~ (kPa)
Pso~(calc) (kPa)
T* (K)
mso,(aq)(calc) (too( kg - t)
mso,c I- (calc) (mol- kg - i)
0.001 0.001 0.001 0.001 0.010 0.010 0.010 0.010 0.010 0.050 0.050 0.050 0.050 0.100 0.100 0. 100 0.100 0.100 0.100 0.500 0.500 0.500 0.500 1.000 1.000 1.000 1.000
298.15 298.15 298.25 298.15 298.15 298.25 298.25 298.15 298.25 298.25 298.15 298.15 298.45 298.35 298.35 298.25 298.25 298.25 298.15 298.15 298.25 298.15 298.25 297.95 298.15 298.15 298.05
0.00150 0.00530 0.00863 0.01176 0.00114 0.00433 0.00748 0.01052 0.01052 0.00086 0.00347 0.00608 0.00854 0.00081 0.00081 0.00322 0.00565 0.00805 0.00807 0.00081 0.00296 0.00534 0.00753 0.00087 0.00501 0.00674 0.01002
0.016 0.102 0.210 0.327 0.035 0.147 0.273 0.394 0.398 0.050 0.196 0.347 0.502 0.052 0.052 0.210 0.369 0.528 0.526 0.060 0.223 0.389 0.552 0.059 0.348 0.467 0.705
0.016 0.103 0.211 0.328 0.036 0.149 0.274 0.402 0.404 0.050 0.202 0.355 0.506 0.054 0.054 0.214 0.375 0.535 0.534 0.059 0.216 0.388 0.549 0.061 0.351 0.472 0.699
297.45 297.55 297.75 297.65 297.65 297.45 297.65 297.75 297.65 297.85 297.55 297.55 297.85 297.75 297.75 297.65 297.65 297.65 297.55 297.65 297.95 297.65 297.45 297.95 297.95 298.15 297.95
0.00019 0.00125 0.00257 0.00400 0.00044 0.00180 0.00333 0.00491 0.00491 0.00061 0.00247 0.00434 0.00612 0.00066 0.00066 0.00261 0.00458 0.00654 0.00655 0.00072 0.00264 0.00477 0.00672 0.00075 0.00431 0.00580 0.00862
0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00001 0.00001 0.00001 0.00000 0.00002 0.00003 0.00005 0.00001 0.00001 0.00004 0.00007 0.00010 0.00010 0.00005 0.00020 0.00035 0.00050 0.0001 I 0.00062 0.00083 0.00123
characteristic peak of a light absorbing component can be interpreted as one principal component. If there are two components that absorb light of the same or similar wavelength region their peaks will interfere additionally. In this case, the application of PCA gives the information that there are two principal components necessary to explain the whole data set. The graphical representation of the new coordinate system, where PC~ and PC 2 represent the axis, is called 'score plot'. Measurements (objects) with similar behaviour build up special groups or patterns in the score plot. Therefore, a score plot can be used to interpret and quantify variations in peak structures. For the practical realisation of PCA, a commercial software called 'Unscrambler' by Camo has been used. To testify our assumption, we look at the score plot diagramme (Fig. 7) for the liquid phase spectra of the SO e + HC1 + H 2 0 and the SO 2 + CaC12 + H 2 0 systems. It can be seen from Fig. 7 that the spectra of solutions without HC1 and with very small amount of HCI (up to 0.01 tool l - j ) build up one group. With increasing concentration of HC1, separate groups are found. Finally, the spectra of solutions containing 0.5 M CaC12 and 1.0 M HC1 lie in one group. As the two solutions have different HC1 amount and pH value, but the same chloride content, we assume the formation of SO2C1-
230
J. Krissrmmn et aL / Fluid Phase Equilibria 141 (1997) 221-233
0.8 O SO2÷H2O[13]
~..-'"/
X 0.001 mol/l HCI A 0.010 molll HCI
0.6
/
.j'~./
/~/,~// ./~'/.~/" / ...///~/ / .~/.~ / -/~ / / -- -"+/
+ 0.050mol/I HCI [] 0.100mol/I HCI 0.500 mol/l HCl X71.000mol/I HCI
/
/
8
O9
C)
Y//
0.2
00
0.0025
0.005 0,0075 mso2(tot)/(mol/kg)
0.01
0.0125
Fig. 5. Combined phase and chemical equilibrium for SO 2 + HC1 + H 2 0 system at 298 K.
complex instead of S O 2 • HC1 and postulate Eq. (F). As a value for the free energy of formation for SO2CI-(a q) is not available in literature, we fit the equilibrium constant of Eq. (F) to our experimental results. To maintain a physical significance of our treatment, we set the condition that the Lambert-Beer law (cf. Eq. (13)) is fulfilled in the liquid phase and assign an extinction coefficient of 487 tool -1 dm 3 c m - I at 280 nm to SO2(a q) (known through our own investigations on SO 2 + H 2 0 system). A least square minimisation
X3 /
F-structure of scaffered data
centre
X2 Fig. 6. Coordinate transformation by PCA.
231
J. Krissmann et al. / Fluid Phase Equilibria 141 ( 1997i 221-233
O S02+H20 X 0.001mol/I HCI A 0.010mol/I HCI + 0.050mol/I HCI [] 0.100mol/I HCI ?~0.500mol/I HCl ~71.000rnol/I HCI I~ 0,500molll CaCIz
J /,~ / / / /
3.6 2.2
/ ~ J . . r - ~
L.)04 Q_ 0.8
-0.6
-~_
,
I
-6
12
~
I
,
O
I
6
,
I
12
,
I
18
,
24
PC 1 Fig. 7. Score plot diagramme for the uv-spectra of SO 2 + HCI + H 2° and SO 2 + CaC1, + H 2° systems.
t Pso2.m
tt
( Pso2 - Pso2(calc)) 2
17 SO2+ HCI+ H20
( E 28° - E28°(calc)) 2 ~ Minimum
Em
n
(14)
so 2+ HCI+ H2 °
is used for the fit. The PSO2,m and E 2s° are the arithmetic averages of the partial pressure of SO 2 ( P s o .... ) and the absorbance of the solution at 280 nm (E28°), respectively. The equilibrium constant K F, the molar extinction coefficient e(SOzC1-) and the parameter /3(°)(H +, SO2C1-) are thus obtained. The corresponding value of /3 o) is calculated using the empirical correlation [10] /3 ~l~ = 0.018 + 3.06./3 (0)
(115)
The results are listed in Table 2. For the molar extinction coefficient (SO2C1-) at 280 nm, a value of 2936 mol- ~ dm 3 cm-~ is found for the best fit. The calculated values for the absorption of sulfur dioxide in dilute aqueous hydrochloric acid solutions are given in Table 3 and Fig. 6. The phase and chemical equilibrium is described in a convincing way. Published solubility data for SO 2 + HC1 + H20 system in the concentration range studied here, to which our data could be compared, are not available. It may be pointed out here that an investigation of the gas phase alone would not have indicated the formation of a complex like SOzCI- in the liquid phase. This emphasises the need of a simultaneous analysis of the vapour and the liquid phase for a deeper insight into the combined phase and reaction equilibrium.
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J. Krissmann et al. / Fluid Phase Equilibria 141 (1997) 221-233
5. List of symbols
A~ c
I a
f m
P T R x Z
MH2O
E d r/
Debye-Hiickel parameter (kg mol-l)°5 Concentration (mol dm -3) Ionic strength (mol kg -1) Activity ( - ) Fugacity ( - ) Molality in liquid phase (mol kg -1) Pressure (kPa) Temperature (K) Molar gas constant (J mol-1 K - l ) Mole fraction ( - ) Number of charges ( - ) Molecular weight of water (kg mol- J ) Extinction ( Optical path length (cm) Number of measurements
Greek letters Ol
.y E
A
Degree of dissociation Binary interaction parameter Activity coefficient Fugacity coefficient ( - ) Molar extinction coefficient (mol- l dm 3 cm- l) Wavelength (nm)
Superscripts 0 6)
Reference state (pO= 100 kPa, m° = 1 tool kg-~) Standard state of the pure substance
Subscrip~
H20 i,j,k
SO2 aq tot IV, VI 2 m
Water Species i, j or k Sulphur dioxide Aqueous Total Valency Equilibrium Arithmetic average
J. Krissmmn et al. /Fluid
Phase Equilibria 141 (I 9971 221-233
233
References [I] M.A. Siddiqi, J. Krissmann, P. Peters-Gerth, M. Luckas, K. Lucas, J. Chem. Thermodyn. 28 (1996) 685-700. [2] Landolt-Bornstein, Zahlenwerte und Funktionen aus Naturwissenschaft und Technik, Springer, Berlin, Vol. I (b), 1977. [3] R.N. Goldberg, V.B. Parker, J. Res. NBS 90 (1985) 341-358. [4] D. Filippou, G.P. Demopulos, V.G. Papangelakis, AIChE J. 4 1 (1995) 17 1- 184. [5] T. Hunger, F. Lapique, A. Storck, J. Chem. Eng. Data 35 (1990) 453-463. 161 K.S. Pitzer, R.N. Roy, L.F. Silvester, J. Am. Chem. Sot. 99 (1977) 4930-4936. 171 M. Luckas, D. Eden, AIChE J. 41 (1995) 104-1043. [8] K.S. Pitzer, J. Phys. Chem. 77 (1973) 268-277. [9] KS. Pitzer, J.J. Kim, J. Am. Chem. Sot. 96 (1974) 5701-5706. [IO] T.J. Edwards, G. Maurer, J. Newman, J.M. Prausnitz, AIChE J. 24 (1978) 966-976. [ 111 K.S. Pitzer, Activity Coefficients in Electrolyte Solutions, CRC Press, Boca Raton, 1991. [12] C.C. Chen, HI. Britt, J.F. Boston, L.B. Evans, AIChE J. 28 (1982) 588-596. [14] M. Ishibashi, Y. Yamamoto, Y. Inoue, Bull. Inst. Chem. Res. Kyoto Univ. 37 (1959) l-7. [l5] V.B. Parkinson, Tappi 39 (1956) 517-519. [I61 H.F. Johnstone, P.W. Leppla, J. Am. Chem. Sot. 56 (1934) 2233-2238. [ 171 A. Salama, S.B. Salama, M. Sobeir, S. Wasif, J. Chem. Sot. A (197 I), 1112- 1I 17. [ 181 E. Milanova, R.L. Benoit, Can. J. Chem. 55 (1977) 2807-2812. [19] T.G. Burke, D.F. Smith, J. Mol. Spectrosc. 3 (1959) 381-387. [20] S. Witekowa, Z. Chem. 2 (1962) 315-316. [21] M.A. Siddiqi, J. Krissmann, K. Lucas, Fluid Phase Equilibria (1997) in press. [22] H. Martens, T. Naes, Multivariate Calibration, Wiley, New York, 1993. [23] S. Wold, K. Esbenson, P. Geladi, Chem. Int. Lab. Sys. 2 (1987) 37-52.
Fluid Phase Equilibria 141 (1997) 221-233
Absorption of sulfur dioxide in dilute aqueous solutions of sulfuric and hydrochloric acid J. Krissmann *, M.A. Siddiqi, K. Lucas Department q)cThermodynamics, FB 7, Gerhard Mercator University Duisburg, Duisburg 47048, Germany
Received 3 March 1997; accepted 14 August 1997
Abstract Spectrophotometric measurements of combined phase and chemical equilibrium have been performed for S O 2 + HzSO 4 -F H 2 0 and SO 2 + HCI + H 2 0 systems at 298 K and atmospheric pressure. The vapour and liquid phases have been analysed in situ using a fibre optic based technique described in an earlier publication. The measurements have been performed up to an equilibrium partial pressure of about 1 kPa for sulfur dioxide. The concentration range of the acids have been varied up to 0.5 M for H 2 S O 4 and 1.0 M for HCI. A thermodynamic model is presented which allows the interpolation and the extrapolation of the experimental results. The calculated partial pressures of SO 2 in the SO 2 + H2SO 4 + H 2 0 system are compared with existing literature values. The experimental results for the SO 2 + HCI + H 2 0 system show an anomaly in the uv-spectrum of molecular dissolved sulfur dioxide. The absorption band for SO 2 is shifted towards higher wavelength. This effect is interpreted in terms of the formation of a weak complex SO2C1-. © 1997 Elsevier Science B.V. Kevwords: Vapour-liquid equilibria; Chemical equilibria; Spectroscopy; Data; Method of calculation
1. Introduction Flue gases from coal fired power plants or incinerating plants contain pollutants like SO 2 and HCl. A typical way to remove these pollutants is the wet flue gas desulfurisation, which is a complex physical and chemical absorption process. In technical applications, part of the liquid is often recirculated within the absorber. As a consequence of this, there is an increase of the amount of chloride and sulfate ions in relation to the dissolved sulfur dioxide. There is a lack of reliable data for such important binary and ternary systems in literature.
* Corresponding author. 0378-3812/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S 0 3 7 8 - 3 8 1 2 ( 9 7 ) 0 0 2 0 3 - 3
222
J. Krissmann et al. /
Fluid Phase Equilibria 141 (1997) 221-233
Therefore, spectrophotometric measurements of the phase and chemical equilibrium for certain selected systems containing SO 2 have been performed. For this, a newly developed apparatus, which allows the simultaneous in situ analysis of gas and liquid phase, has been used to determine the equilibrium partial pressure of SO 2 and the amount of molecular dissolved sulfur dioxide in SO 2 + H2SO 4 + H 2 0 and SO 2 + HC1 + H20 systems. It is shown that the additional specification of the liquid phase yields a deeper insight into the reactions occurring in solution. A thermodynamic model based on Pitzer's theory is presented to correlate and extrapolate the experimental results.
2. Experimental procedure The measurements were carried out using the apparatus described in a previous communication [ 1]. This apparatus was placed inside an air thermostat to accomplish the measurements at a constant temperature of 298 K. Standard gas mixtures from Messer-Griesheim with an uncertainty of _+0.5% were used to prepare the gaseous mixtures of desired compositions. The acidic solutions were prepared from certified molar mixtures of acids from Fluka (accuracy better than ± 0.1%) by diluting these with deionised water. The solution was degassed with nitrogen, which was saturated with H20 by bubbling through deionised water, to remove any dissolved carbon dioxide and oxygen. The concentration of the aqueous solution was checked additionally using ion chromatography for chloride and sulfate ions. As the calculations are done on a molal basis, the molarities of the solutions were converted to molalities using tabulated density data [2]. The method for the measurements was basically the same as described earlier except that this time the simultaneous analysis of the liquid phase was performed by circulating it via insulated tubing through a standard cuvette placed inside another uv-spectrophotometer (Shimadzu UVPC 2102). With increasing acid concentrations, it was necessary to use an optical length of 1 mm to cope with the high absorbance by the solutions. The reaction was started by opening the appropriate valves and circulating the gas mixture through the aqueous solution. After attainment of the thermodynamic equilibrium (indicated by a non-changing spectrum over a period of time), the spectrum of the gaseous phase was taken by scanning through the wavelength range of 220 nm to 400 nm with the help of the uv-diode array spectrophotometer and evaluated as described before [1] to determine the concentration of sulfur dioxide in the vapour phase, C 2 (SO2), in equilibrium with the liquid. The equilibrium partial pressure (reference pressure: p0 = 100 kPa), was then calculated by p0
p(SO2)/kPa = --. P2
6 2 ( 8 0 2 ) . R- T2
(1)
where P2, T2 and C 2 (802) denote the pressure (kPa), temperature (K) and SO 2 concentration in the gas phase (mol dm -3) at equilibrium. Finally, the spectrum of the liquid phase (220-400 nm) was taken by circulating it through the cuvette of the second uv-spectrophotometer. Evaluation of this spectrum furnished the specification of the liquid phase. The calibration for the liquid phase depends on the components present and will be described in context with the results.
J. Krissmann et al. / Fluid Phase Equilibria 141 ~1997) 221-233
.-3
3. Thermodynamic model The absorption of sulfur dioxide in aqueous solutions of H2SO 4 and HCI in the absence of oxygen can be described using the following equations SO2(g) ~ SO2(aq )
(A)
SO2(aq) + H20(1 ) ~ H+(aq) + HSO3(aq)
(B)
HeSO4(aq ) ~ H+ (aq) + HSOa(aq)
(c)
HSO 4 (aq) ~ H + (aq) + SO 2- (aq)
(D)
nCl(aq) ~ H+(aq) + Cl-(aq)
(E)
SO2(aq) ~ Cl-(aq) ~ SO2Cl-(aq)
(F)
and
Eqs. (A) and (B) describe the physical absorption and the hydrolysis of sulfur dioxide [3]. The formation of sulfite (SO 2 ) and pyrosulfite ion ($20~-) is neglected because of the low pH of the solution and the low concentrations for SO 2 [1]. The first dissociation of sulfuric acid, Eq. (C), is assumed to be complete in the concentration range studied here [4,5], whereas for the second dissociation (Eq. (D)) the equilibrium constant is adopted from Pitzer's work [6]. The dissociation of the hydrogen chloride (Eq. (E)) is assumed to be complete as well, because of the high dilution [7]. Finally, Eq. (F) shows the formation of the weak complex SO2C1 . The justification for this reaction follows later in this section. Based on the assumed reaction scheme, the equilibrium constants for Eqs. (A), (B), (D) and (F) can be formulated as (-/so ~
,)/SO2(aq )
mso2(aq)
p0
4'so
Pso
""
KA(T) = fso. xB(r) =
a H , • aHSOg
,.,
=
aSO2(a q) " a H , O
KD(T ) .
aH+'aso~ . aso,c, aSO_,(aq) " a c I
"yH +" a/HSO g
m H ~" mHSO{
1
")/SOe(aq) " ")/H ~O
mso2(aq) " XH ,O
roll
TH+" Yso~ . .
mH+' mso ~
1
")/HSO£
mHSQ
mO
~-/HSO ~
KF(T ) =
(2)
=
Yso,o
mso,c,
'YSO2(aq) " ")/CI
m s o z ( a q ) " Ill('1
(3)
~'4) • m"
(5)
Here, (9 denotes the standard state of the pure substance, pO = 100 kPa and m ° = 1 tool kg ~. The mass balance for S ~v, S vl and C1 gives mso~_(tot ) = mso2(aq ) Jr- mHSO7 q-
msoec I
(6)
224
J. Krissmann et al. / Fluid Phase Equilibria 141 (1997) 221-233
+ m(0) H2SO 4 = mHSO2 msog-
(7)
m(0) HC1 ~
(8)
mCl-
+
mso2cl
and the condition of electroneutrality for the solution leads to mn+-mcl -2.mso ~ -mnso;-mns
(9)
Q - - m s o ~ cr- = 0 .
The gas phase is treated like an ideal gas. The equilibrium concentrations of the species existing in the liquid phase may be obtained by solving these equations. However, the activity coefficients are not directly known. Starting from Pitzer's theory [8,9], considering the ion-ion, ion-molecule and molecule-molecule interactions and following the treatment of Edwards et al. [10], the following equation for the activity coefficient of any species i (ionic or molecular) is used lnyi=
-As(T)"
( f[ 1 ln(l+l,2fi))+2 z2 1 + 1,2~/I" + 1,----2
×(1-(1
+ 2v~)exp(-Zfi)))
z2 Y'.
412 jv~H20
" ~ ,nj(/3i~°)+ 13~jz) j~n2o 2--7-
Y'~ mjm~j~)(1-(1
+ 2v~ + 21)
k~H20
× exp( - 2v~)) Here,
z i denotes
(10)
the charge of the component i and I is the ionic strength of the solution, given as
1
I= -~" Y'~mi.zZi
(11)
i
The first term of Eq. (10) is derived from Debye-Htickel theory and describes the strong coulomb forces between the ions. The short range interactions between ion-ion, ion-molecule and moleculemolecule are represented by the other two terms. This model takes into account only the binary interaction parameters, which is justified for the low solute concentrations studied here [8]. The parameters for the ion-ion interaction are taken from literature for strong electrolytes [11,5], while the molecule-molecule and the molecule-ion interaction parameters are neglected. The parameter /3 (0) for the interaction between H + and SO2CI- does not exist in the literature and was, therefore, fitted to reproduce our results. Following Pitzer, the short range interaction parameters between ions of the same charge are set equal to zero. The Debye-Hiickel term is also a function of temperature and is taken from the work of Chen et al. [12]. Finally, the water activity is calculated as [10]
lna°n2o=Mn2o
( 2A~(T)'II5 1+i'_2~¢ff
-
y'~
]~
) mimj(~iT)+C3iT)exp(-Zv/-[))
i~e H20 j ~ H 2 0
-Mn2 o ~
mi
(12)
i~H20
The calculation is done iteratively, because the activity coefficients depend on the ionic strength which is itself a function of the molalities. The iteration is done until the activity coefficients of the solutes do not change significantly. The partial pressure can then be calculated from Eq. (2).
.-5
J. Krissmann et al. / Fluid Phase Equilibria 141 (1997) 221-233
4. Results and discussion The experimental results for the partial pressure of SO 2 and the molality of undissociated sulfur dioxide mso2(aq ) in the SO 2 + H2SO 4 + H 2 0 system are shown in Table 1 and Figs. 1 and 2. The ion-ion interaction parameters used for the calculations are taken from literature and are listed in Table 2. The experimental and calculated values match very well. An influence of H 2 S Q on the uv-spectrum has been reported in more concentrated sulfuric acid [ 14]. At low H 2SO4 concentrations studied in this work, no such effect was noticed (cf. Fig. 2). Using this thermodynamic model, further calculations are done at other temperatures for a comparison with literature data. Parkinson [15] measured the solubility of SO 2 in water and aqueous solutions containing 0.058 M sulfuric acid at various temperatures. His results can be reproduced by our model within experimental error (Fig. 3). This places confidence in the extrapolation ability of the described model in terms of molality mso2ctot) and temperature. The temperature effect could be adequately described by considering the temperature dependence of Debye-H~ickel term and of the equilibrium constants of Eqs. (A), (B) and (D). The ion-ion interaction parameters are considered
Table I Phase and chemical equlibrium for SO 2 + H2SO 4 + H20 system CH~sQ (mol d i n - 3)
mso,oo, ) (tool kg - t )
T (K)
0.005 0.005 0.005 0.005 0.005 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.100 0. 100 0.100 0.100 0.100 0.51)0 0.500 0.500 0.500 0.500
0.00123 0.00455 0.00761 0.01066 0.01545 0.00092 0.00097 0.00335 0.00495 0.00593 0.00596 0.00824 0.01237 0.01253 0.00079 0.00401 0.00483 0.00787 0.01163 0.00081 0.00316 0.00485 0.00740 0.01112
298.35 298.55 298.05 298.35 298.25 298.25 298.05 298.45 298.15 298.35 298.15 298.25 298.05 298.15 298.15 298.15 298.05 298.15 298.15 298.15 298.25 298.05 298.05 298.25
Pso~ (kPa)
Pso2(calc) (kPa)
T * (K)
0.033 0.140 0.254 0.373 0.592 0.051 0.054 0.200 0.302 0.349 0.357 0.512 0.770 0.765 0.053 0.267 0.317 0.533 0.800 0.064 0.249 0.375 0.572 0.864
0.035 0.144 0.254 0.382 0.592 0.057 0.059 0.208 0.304 0.368 0.367 0.510 0.761 0.774 0.054 0.275 0.330 0.541 0.799 0.063 0.248 0.378 0.576 0.873
298.35 298.55 298.25 298.35 298.15 298.25 298.05 298.45 298.15 298.35 298.15 298.25 298.05 297.95 297.95 297.75 297.85 298.05 297.95 297.85 297.75 297.75 297.85 297.65
T* is the temperature of solution in the cuvette.
tHSO2(aq) I)
/nSO2(aq t(calc) I)
(tool kg
(mol kg -
-
0.00042 0.00175 0.00313 0.00466 0.00724 0.00069 0.00073 0.00253 0.00374 0.00448 0.00450 0.00624 /).00938 0.00950 0.00067 0.00338 0.00407 0.00664 0.00981 0.00078 0.00303 0.00466 0.00710 0.01067
0.00321 0.00738 0.00068 0.00369 0.00949 0.00960 0.00067 0.00336 0.00413 0.00660 0.00983 0.00080 0.00305 0.00464 0.00708 0.01067
J. Krissmann et al. / Fluid Phase Equilibria 141 (1997) 221-233
226
1, X 0.005rnolfl H2SO4 + 0.050mol/I H2SO4
0.8
/~ /
[] O.lOOmot/,.,so,
/
A 0.500mol;I HzSO4
/
/ ~
/ ,./
/ /
/
/
~_ 0.6
y_o.4
0.2
I
00
~
0.003
I
,
I
L
i
0.006 0.009 0.012 mso2(tot] / (mol/kg)
,
I
,
0.015
0.018
Fig. I. Combinedphase and chemicalequilibriumfor SO2 + H2SO4 4-H20 systemat 298 K.
independent of temperature. In Fig. 4, the available literature values at 298.15 K are compared with our results. The measurements of Hunger et al. [5] agree with the calculations done with our model, except for one point at 0.03 mol kg -~. The experimental values of Johnstone and Leppla [16] for SO 2 + H 2 0 and SO 2 + H2SO 4 + H 2 0 systems may be reproduced by our model with the exception of very dilute sulfuric acid solutions (0.0879 mol kg-J H2SO4).
0.018 0.015
/-
O SO2+H20[13] X 0.005mol/I H2504 + 0.050mol/I HzSO4
/~/" o
[] 0.100mol/I H,SO4 Z~0.500mol/I H2SO4
"~
/.~ ./~./"
100% SO2(aq) 7 / / ,/7/" j
F
/
. /
/
///,
0.0o9 ~0.006
.... /.
/.
0.003 0
0.003
0.006 0.009 0.012 mso2(lot) / (mol/kg)
0.015
0.018
Fig. 2. Molalityof moleculardissolved S O 2 in SO2 + H2SO4 4-H20 systemat 298 K.
227
J. Krissmann et al. / Fluid Phase Equilibria 141 ( I997~ 221-233
Table 2 Parameters used in the model Equilibrium constants a n d D e b v e - Hiickel p a r a m e t e r at t,arious temperatures
298.15 K
294.25 K
305.35 K
1.228 0.0139 0.0105 O. 162 0.3909
1.421 0.0152 0.0119 -0.3883
0.955 0.{)116 0.0084
i
J
t-~(o, ~ij
H4 n~ H* H H+ All other interaction parameters
HSO:~ HSQ SO~ CISO2C1 are set equal to zero
KA KB KD Kr
A + / ( k g mol- ~)os
0.3962
Source [3] [3] [6] This wc,rk [12]
Interaction p a r a m e t e r s
Source
,G~]'
0.1500 0.2106 0.0217 0.1775 0.1741
0.4000 0.532/) 0.2945 0.5508
[5] [1 I1 [11] [1 I] This work
The experimental results for the SO 2 + HC1 + H 2° system are presented in Table 3 and Fig. 5. An examination of Fig. 5 shows that the partial pressure of SO 2 in the SO~ + HC1 + H+O system increases up to a concentration of 0.5 M HC1, but is lower at 1 M HC1. This decrease at 1 M HCI concentration can not be explained on the basis of the dissociation of SO2(aq). A careful study of the spectra of the liquid phase for the SO 2 + HC1 + H 2 0 system reveals that the uv-spectra show a
© 294.25K, SO2+H20 A 294.25K, 0.0580mol/IH2SO4 [] 305.35K, 0.0580mol/IHzSQ ~v3 Model ~
/" /
/
U ~
~
G_ "--2 cO
G_ 1
00
i 0.02
0.04
0.06
ms02(tot) / (mol/kcj) Fig. 3. Comparison of model calculations with literature data [ 15] at various temperatures.
228
J.
Krissmann et al. / Fluid Phase Equilibria 141 (1997) 221-233
2.5 O SO2+H20[16] [] 0.0879mol/kg H2SO4 [10] A 0.5174mol/kg H2SO4 [163 2 ~ 7 $.[030 mollkg H2SO4 [16] ...... Model • so,+mo
[5]
t ~ • 0.01 mol/I H2SO, [5] CL- J " o " -,z i , 0.20 m ol/I H2SO` [5] Model - ~
-
,//S~..'"
J
// ~
~
/
/ /
/
,./-."
0
,
-0
(fZ//..//
,,:~.// //" ;x-y,'" ,.,, ..
,,.¢~-//,"'" // // (///~////
-
05 -
,SS'~// / / / //////-/ /// ///,,/"~/"/
-
I
0.01
,
I
,
0.02 mso2(tot) / ( m o l / k g )
I
0.03
J
0.04
Fig. 4. Comparisonof model calculationswith literaturedata [5,16] at 298 K.
change in the peak structure depending upon the amount of hydrogen chloride in solution, when compared with the spectrum of molecular dissolved sulfur dioxide in pure water. It is observed that there is a shift of the peak maximum to greater wavelength (from 276 nm to nearly 280 nm) with increasing HC1 content in the solution. We attribute the above mentioned effects to be caused by the formation of a weak complex SOzC1-. The complexation of sulfur dioxide by halides ( S O z X - ) in acetonitrile, water and dimethyl sulfoxide solutions has been reported in the literature [17,18]. The formation of a complex like SO 2 • HC1 in aqueous solutions as well as in the vapour phase is also documented [19,20]. Both of these complexes are stochiometrically possible. In order to testify, whether the amount of total hydrogen chloride or chloride ion only is responsible for the described anomaly, we compare the liquid phase spectra for the SO 2 + HC1 + H 2 0 system and those for the SO 2 + CaC12 + H 2 0 system, reported elsewhere [21]. It is seen that both spectra are very much similar. To quantify this, a special mathematical algorithm called 'principal component analysis' (PCA) [22,23] is applied for comparison of the liquid phase spectra. The essential requirement for PCA is the existence of linear interactions between the variables. In uv-spectroscopy the Lambert-Beer law describes such a linear connection between the concentration of the light absorbing component i and the extinction
E(a)=
= i
c,.a
(13)
i
The assumption of a linear behaviour leads to the possibility of data reduction by transformation to a new appropriate coordinate system. The new axis (Fig. 6) lies in the direction of the maximum variation in the data set and is called principal component (PC~). In uv-spectroscopy, the whole
229
J. Krissmann et al. / Fluid Phase Equilibria 141 (1997) 221-233
Table 3 Phase and chemical equilibrium for SO 2 + HC1 + H 20 system CHCl 3) (tool dm
T (K)
mso:(tot) (tool kg- i )
Pso~ (kPa)
Pso~(calc) (kPa)
T* (K)
mso,(aq)(calc) (too( kg - t)
mso,c I- (calc) (mol- kg - i)
0.001 0.001 0.001 0.001 0.010 0.010 0.010 0.010 0.010 0.050 0.050 0.050 0.050 0.100 0.100 0. 100 0.100 0.100 0.100 0.500 0.500 0.500 0.500 1.000 1.000 1.000 1.000
298.15 298.15 298.25 298.15 298.15 298.25 298.25 298.15 298.25 298.25 298.15 298.15 298.45 298.35 298.35 298.25 298.25 298.25 298.15 298.15 298.25 298.15 298.25 297.95 298.15 298.15 298.05
0.00150 0.00530 0.00863 0.01176 0.00114 0.00433 0.00748 0.01052 0.01052 0.00086 0.00347 0.00608 0.00854 0.00081 0.00081 0.00322 0.00565 0.00805 0.00807 0.00081 0.00296 0.00534 0.00753 0.00087 0.00501 0.00674 0.01002
0.016 0.102 0.210 0.327 0.035 0.147 0.273 0.394 0.398 0.050 0.196 0.347 0.502 0.052 0.052 0.210 0.369 0.528 0.526 0.060 0.223 0.389 0.552 0.059 0.348 0.467 0.705
0.016 0.103 0.211 0.328 0.036 0.149 0.274 0.402 0.404 0.050 0.202 0.355 0.506 0.054 0.054 0.214 0.375 0.535 0.534 0.059 0.216 0.388 0.549 0.061 0.351 0.472 0.699
297.45 297.55 297.75 297.65 297.65 297.45 297.65 297.75 297.65 297.85 297.55 297.55 297.85 297.75 297.75 297.65 297.65 297.65 297.55 297.65 297.95 297.65 297.45 297.95 297.95 298.15 297.95
0.00019 0.00125 0.00257 0.00400 0.00044 0.00180 0.00333 0.00491 0.00491 0.00061 0.00247 0.00434 0.00612 0.00066 0.00066 0.00261 0.00458 0.00654 0.00655 0.00072 0.00264 0.00477 0.00672 0.00075 0.00431 0.00580 0.00862
0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00001 0.00001 0.00001 0.00000 0.00002 0.00003 0.00005 0.00001 0.00001 0.00004 0.00007 0.00010 0.00010 0.00005 0.00020 0.00035 0.00050 0.0001 I 0.00062 0.00083 0.00123
characteristic peak of a light absorbing component can be interpreted as one principal component. If there are two components that absorb light of the same or similar wavelength region their peaks will interfere additionally. In this case, the application of PCA gives the information that there are two principal components necessary to explain the whole data set. The graphical representation of the new coordinate system, where PC~ and PC 2 represent the axis, is called 'score plot'. Measurements (objects) with similar behaviour build up special groups or patterns in the score plot. Therefore, a score plot can be used to interpret and quantify variations in peak structures. For the practical realisation of PCA, a commercial software called 'Unscrambler' by Camo has been used. To testify our assumption, we look at the score plot diagramme (Fig. 7) for the liquid phase spectra of the SO e + HC1 + H 2 0 and the SO 2 + CaC12 + H 2 0 systems. It can be seen from Fig. 7 that the spectra of solutions without HC1 and with very small amount of HCI (up to 0.01 tool l - j ) build up one group. With increasing concentration of HC1, separate groups are found. Finally, the spectra of solutions containing 0.5 M CaC12 and 1.0 M HC1 lie in one group. As the two solutions have different HC1 amount and pH value, but the same chloride content, we assume the formation of SO2C1-
230
J. Krissrmmn et aL / Fluid Phase Equilibria 141 (1997) 221-233
0.8 O SO2÷H2O[13]
~..-'"/
X 0.001 mol/l HCI A 0.010 molll HCI
0.6
/
.j'~./
/~/,~// ./~'/.~/" / ...///~/ / .~/.~ / -/~ / / -- -"+/
+ 0.050mol/I HCI [] 0.100mol/I HCI 0.500 mol/l HCl X71.000mol/I HCI
/
/
8
O9
C)
Y//
0.2
00
0.0025
0.005 0,0075 mso2(tot)/(mol/kg)
0.01
0.0125
Fig. 5. Combined phase and chemical equilibrium for SO 2 + HC1 + H 2 0 system at 298 K.
complex instead of S O 2 • HC1 and postulate Eq. (F). As a value for the free energy of formation for SO2CI-(a q) is not available in literature, we fit the equilibrium constant of Eq. (F) to our experimental results. To maintain a physical significance of our treatment, we set the condition that the Lambert-Beer law (cf. Eq. (13)) is fulfilled in the liquid phase and assign an extinction coefficient of 487 tool -1 dm 3 c m - I at 280 nm to SO2(a q) (known through our own investigations on SO 2 + H 2 0 system). A least square minimisation
X3 /
F-structure of scaffered data
centre
X2 Fig. 6. Coordinate transformation by PCA.
231
J. Krissmann et al. / Fluid Phase Equilibria 141 ( 1997i 221-233
O S02+H20 X 0.001mol/I HCI A 0.010mol/I HCI + 0.050mol/I HCI [] 0.100mol/I HCI ?~0.500mol/I HCl ~71.000rnol/I HCI I~ 0,500molll CaCIz
J /,~ / / / /
3.6 2.2
/ ~ J . . r - ~
L.)04 Q_ 0.8
-0.6
-~_
,
I
-6
12
~
I
,
O
I
6
,
I
12
,
I
18
,
24
PC 1 Fig. 7. Score plot diagramme for the uv-spectra of SO 2 + HCI + H 2° and SO 2 + CaC1, + H 2° systems.
t Pso2.m
tt
( Pso2 - Pso2(calc)) 2
17 SO2+ HCI+ H20
( E 28° - E28°(calc)) 2 ~ Minimum
Em
n
(14)
so 2+ HCI+ H2 °
is used for the fit. The PSO2,m and E 2s° are the arithmetic averages of the partial pressure of SO 2 ( P s o .... ) and the absorbance of the solution at 280 nm (E28°), respectively. The equilibrium constant K F, the molar extinction coefficient e(SOzC1-) and the parameter /3(°)(H +, SO2C1-) are thus obtained. The corresponding value of /3 o) is calculated using the empirical correlation [10] /3 ~l~ = 0.018 + 3.06./3 (0)
(115)
The results are listed in Table 2. For the molar extinction coefficient (SO2C1-) at 280 nm, a value of 2936 mol- ~ dm 3 cm-~ is found for the best fit. The calculated values for the absorption of sulfur dioxide in dilute aqueous hydrochloric acid solutions are given in Table 3 and Fig. 6. The phase and chemical equilibrium is described in a convincing way. Published solubility data for SO 2 + HC1 + H20 system in the concentration range studied here, to which our data could be compared, are not available. It may be pointed out here that an investigation of the gas phase alone would not have indicated the formation of a complex like SOzCI- in the liquid phase. This emphasises the need of a simultaneous analysis of the vapour and the liquid phase for a deeper insight into the combined phase and reaction equilibrium.
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J. Krissmann et al. / Fluid Phase Equilibria 141 (1997) 221-233
5. List of symbols
A~ c
I a
f m
P T R x Z
MH2O
E d r/
Debye-Hiickel parameter (kg mol-l)°5 Concentration (mol dm -3) Ionic strength (mol kg -1) Activity ( - ) Fugacity ( - ) Molality in liquid phase (mol kg -1) Pressure (kPa) Temperature (K) Molar gas constant (J mol-1 K - l ) Mole fraction ( - ) Number of charges ( - ) Molecular weight of water (kg mol- J ) Extinction ( Optical path length (cm) Number of measurements
Greek letters Ol
.y E
A
Degree of dissociation Binary interaction parameter Activity coefficient Fugacity coefficient ( - ) Molar extinction coefficient (mol- l dm 3 cm- l) Wavelength (nm)
Superscripts 0 6)
Reference state (pO= 100 kPa, m° = 1 tool kg-~) Standard state of the pure substance
Subscrip~
H20 i,j,k
SO2 aq tot IV, VI 2 m
Water Species i, j or k Sulphur dioxide Aqueous Total Valency Equilibrium Arithmetic average
J. Krissmmn et al. /Fluid
Phase Equilibria 141 (I 9971 221-233
233
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